Contra Costa College
Course Outline
Department & Number MATH-185
Course Title Discrete Mathematics
Prerequisite MATH-171 or both MATH-121 and
MATH-135
Challenge Policy Satisfactory completion of equivalent
course or courses at another institution
Co-requisite
Challenge Policy
Advisory
*HOURS BY ARRANGEMENT:
0
Number of Weeks 18
Lecture Hours By Term 54
Lab Hours By Term 0
*Hours By Arrangement
0
Units
3
Hours per term.
ACTIVITIES: (Please provide a list of the activities students will perform in order to satisfy the HBA
requirement):
COURSE/CATALOG DESCRIPTION
This course covers fundamental topics for Computer Science, such as logic, proof techniques, sets, introduction to
computer programming, basic counting rules, relations, functions and recursion, graphs and probability trees.
This course meets the CSU General Education requirement for Area B4-Mathematics/Quantitative Reasoning, and
the IGETC for Area 2: Mathematical Concepts and Quantitative Reasoning. Emphasis will be on topics of interest to
students of computer science and mathematics.
COURSE OBJECTIVES:
At the completion of the course the student will be able to:
1. Use recursion to analyze algorithms and programs;
2. Write proofs using symbolic logic and Boolean Algebra;
3. Use sets to solve problems in combinatorics and probability theory;
4. Apply matrices to analyze graphs and trees; and
5. Use finite state machines to model computer operations.
INTENDED STUDENT LEARNING OUTCOMES:
1.
2.
3.
4.
5.
Students will be able to use the laws of formal logic and the rules of logical inference to analyze the
validity of a formal argument.
Students will be able to apply proof techniques, including mathematical induction, to prove results
from elementary number theory.
Students will be able to construct and carry out traversal algorithms on graphs, including binary
trees.
Students will be able to construct and determine the output of computational structures including
logic circuits and deterministic finite automata.
Students will be able to carry out recursive algorithms, including the Euclidean Algorithm.
COURSE CONTENT (Lecture):
1. Formal logic including statements, symbolic representation, tautologies, propositional logic,
quantifiers, predicates, and validity, predicate logic, and logic programming;
2. Proofs, recursion, and analysis of algorithms including proof techniques, proof by induction, proof
of correctness programming, recursive definitions, recurrence relations, and analysis of algorithms;
3. Sets, combinatorics, probability, and number theory including counting, principle of inclusion and
exclusion; Pigeonhole Principle, permutations and combinations, and Binomial Theorem;
4. Relations, functions, and matrices including relations and databases, modular arithmetic;
5. Graphs and trees including graphs and their representations, trees and their representations, decision
trees, and Huffman Codes;
6. Graph algorithms including directed graphs and binary relations; Warshall’s algorithm, Euler Path
and Hamiltonian Circuit, shortest path and minimal spanning tree, traversal algorithms, and
articulation points and computer networks;
7. Boolean Algebra and computer logic including Boolean algebra structure, logic networks, and
minimization; and
8. Modeling arithmetic, computation, and languages including algebraic structures, finite-state
machines, and formal languages.
COURSE CONTENT (Lab):
METHODS OF INSTRUCTION:
Lecture and discussion
Demonstration and collaboration
Daily reading assignments
Homework exercises
INSTRUCTIONAL MATERIALS:
NOTE: To be UC/CSU transferable, the text must be dated within the last 7 years OR a statement of
justification for a text beyond the last 7 years must be included.
Textbook Title:
Author:
Publisher:
Edition/Date:
Textbook Reading Level:
Justification Statement:
Discrete Mathematics and Its Applications
Kenneth H. Rosen
McGraw-Hill
Seventh Edition / 2012
(For textbook beyond 7 years)
Lab Manual Title (if applicable):
Author:
Publisher:
Edition/Date:
OUTSIDE OF CLASS WEEKLY ASSIGNMENTS:
Title 5, section 55002.5 establishes that a range of 48 -54hours of lecture, study, or lab work is required for one
unit of credit. For each hour of lecture, students should be required to spend an additional two hours of study
outside of class to earn one unit of credit.
 State mandates that sample assignments must be included on the Course Outline of Record.
Outside of Class Weekly Assignments
Hours per week
Weekly Reading Assignments (Include detailed assignment below, if
applicable)
3
Students are responsible for reading the sections of the textbook corresponding to the week’s
lectures. The number of sections covered per week may vary between 2 and 5. For the adopted
text listed above, this translates to approximately 20 – 30 pages of reading per week.
Weekly Writing Assignments (Include detailed assignment below, if
applicable)
Weekly Math Problems (Include detailed assignment below, if applicable)
3-6
Students are assigned homework exercises by chapter, and are expected to complete the exercises
as the material is covered in lecture. A typical assignment includes approximately 8 problems
per section of the text; this translates to a minimum of between 20 – 40 homework exercises per
week. Note: 3 – 6 hours per week represents the minimum amount of time a student will spend
on homework exercises.
Lab or Software Application Assignments (Include detailed assignment below,
if applicable)
Other Performance Assignments (Include detailed assignment below, if
applicable)
STUDENT EVALUATION: (Show percentage breakdown for evaluation instruments)
 Course must require use of critical thinking, college-level concepts & college-level learning skills.
 For degree credit, course requires essay writing unless that requirement would be inappropriate to the
course objectives. If writing is inappropriate, there must be a requirement of problem-solving or skills
demonstration.
% Essay (If essay is not included in assessment, explain below.)
N/A
25 % Computation or Non-computational Problem Solving Skills
% Skills Demonstration
75 % Objective Examinations
Other (describe)
%
GRADING POLICY: (Choose LG, P/NP, or SC)
X Letter Grade
Pass / No Pass
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
Below 60% = F
70% and above = Pass
Below 70% = No Pass
Prepared by: Carol Stanton, Mathematics
Date: Spring 2014
Revised form 01/14
Student Choice
90% - 100% = A
80% - 89% = B
70% - 79% = C
60% - 69% = D
Below 60% = F
or
70% and above =
Pass
Below 70% = No
Pass